Sadly for Mr Cameron, you are both As a BSc(Econ) European Politics (a few years ago granted) I think that the previous poster has their wires a little crossed

'Every person holding the nationality of a Member State shall be a citizen of the Union. Citizenship of the Union shall be additional to and not replace national citizenship.'

I think the wire crossing may come from the right to apply, as British citizen, to bring a non-EEA spouse/family members into the UK via an EEA country. To circumvent our strict rules you can move to another member state, establish residency there by exercising your treaty rights for six months, and then apply for them to join you. Once they have arrived, you can then move to the UK and bring them with you. As they have a residence permit for another member state, the UK is forced to issue a 5-year permit with minimal fuss.

P.S. Sorry for going OT!